Awkward reflection on mesh
let me adress the issues :).
I also attached a repaired blendfile at the end.

01) The 'sun like' pattern appears when Subdivision Modifier is applied on a triangle fan. Just play a bit with the size of the triangles, or use Face->Grid fill to fill the cap with quads.

02) The edges are harsh, because they are not connected.
You have two meshes joined into one object, but that's not enough. They're just going through each other.
You need to connect the vertices of those two meshes, so they create one continuous mesh.



Other tips for your workflow:
1) There's no need to use Edit cage option in the Subdivision modifier.
In this case it just deforms the mesh without any benefit.
You also don't need 4 levels of subdivision. 2 levels are enough.

Example of my settings


2)  Use milimeters, and absolute grid snapping. It will make your modelling considerably easier, especially when modelling real world objects.

 

3) When using mirror modifier, make sure your mesh is cut in half. Otherwise the mirror modifier will create double-faces which are a pain in the ass to deal with :).
Your original mesh has a few of these.

Here is your repaired Blendfile. Check the differences, and find out which way works best for you.
The meshes are not connected, you'll need to do it yourself.


If you'll need any clarification, let me know.
You're doing great, happy Blendering :).